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Trajectory Optimization Under Stochastic Dynamics Leveraging Maximum Mean Discrepancy

31 January 2025
Basant Sharma
A. K. Singh
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Abstract

This paper addresses sampling-based trajectory optimization for risk-aware navigation under stochastic dynamics. Typically such approaches operate by computing N~\tilde{N}N~ perturbed rollouts around the nominal dynamics to estimate the collision risk associated with a sequence of control commands. We consider a setting where it is expensive to estimate risk using perturbed rollouts, for example, due to expensive collision-checks. We put forward two key contributions. First, we develop an algorithm that distills the statistical information from a larger set of rollouts to a reduced-set with sample size N<<N~N<<\tilde{N}N<<N~. Consequently, we estimate collision risk using just NNN rollouts instead of N~\tilde{N}N~. Second, we formulate a novel surrogate for the collision risk that can leverage the distilled statistical information contained in the reduced-set. We formalize both algorithmic contributions using distribution embedding in Reproducing Kernel Hilbert Space (RKHS) and Maximum Mean Discrepancy (MMD). We perform extensive benchmarking to demonstrate that our MMD-based approach leads to safer trajectories at low sample regime than existing baselines using Conditional Value-at Risk (CVaR) based collision risk estimate.

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@article{sharma2025_2501.19045,
  title={ Trajectory Optimization Under Stochastic Dynamics Leveraging Maximum Mean Discrepancy },
  author={ Basant Sharma and Arun Kumar Singh },
  journal={arXiv preprint arXiv:2501.19045},
  year={ 2025 }
}
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